Ising model on a 2D additive small-world network

In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system consists of $$L\times L$$ square lattice where each site is occupied for spin variable that interacts with nearest neighbor and has certain probability p being additionally connected at random one its farther neighbors. in contact heat bath given temperature T it simulated by one-spin flip according Metropolis prescription. We calculated thermodynamic quantities system, such as magnetization per $$m_{L}$$ , magnetic susceptibility $$\chi _{L}$$ reduced fourth-order Binder cumulant $$U_{L}$$ function several values size L p. also constructed phase diagram equilibrium states plane versus showing existence continuous transition line between ferromagnetic F paramagnetic P phases. Using finite-size scaling (FSS) theory, obtained critical exponents varying parameter p, observed change behavior from regular A-SWN.